K. Timperi

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math.MG2025

$ε$ -neighbourhoods in the Plane with a Nowhere-smooth Boundary

Jeroen S. W. Lamb, Martin Rasmussen, Kalle G. Timperi

We give an example of a planar set $E \subset R^{2}$ for which the boundary $\partial E_{ε}$ of its $ε$ -neighbourhood $E_\varepsilon = \{x \in \mathbb{R}^2…

math.MG2025

On Boundaries of $ε$ -neighbourhoods of Planar Sets, Part II: Global Structure and Curvature

Jeroen S. W. Lamb, Martin Rasmussen, Kalle Timperi

We study the global topological structure and smoothness of the boundaries of $ε$ -neighbourhoods $E_\varepsilon = \{x \in \mathbb{R}^2 \, : \, \textrm{dist}(x, E) \leq \v…

math.MG2025

On Boundaries of $ε$ -neighbourhoods of Planar Sets: Singularities, Global Structure, and Curvature

Jeroen S. W. Lamb, Martin Rasmussen, Kalle G. Timperi

We study the geometry, topological properties and smoothness of the boundaries of closed $ε$ -neighbourhoods $E_\varepsilon = \{x \in \mathbb{R}^2 \, : \, \textrm{dist}(x,…

ε-neighbourhoods in the Plane with a Nowhere-smooth Boundary

On Boundaries of ε-neighbourhoods of Planar Sets, Part II: Global Structure and Curvature

On Boundaries of ε-neighbourhoods of Planar Sets: Singularities, Global Structure, and Curvature

$ε$ -neighbourhoods in the Plane with a Nowhere-smooth Boundary

On Boundaries of $ε$ -neighbourhoods of Planar Sets, Part II: Global Structure and Curvature

On Boundaries of $ε$ -neighbourhoods of Planar Sets: Singularities, Global Structure, and Curvature